Automatic determination of transfer function for ct reconstruction

ABSTRACT

A computer-implemented method of automatically determining photon-count to penetrated depth function for a CT reconstruction includes performing one or more test CT reconstructions on one or more radiographs, each test CT reconstruction using a test transfer function, to provide one more test reconstructions and determining a final transfer function from the one or more test reconstructions.

BACKGROUND

A computed tomography scan (“CT scan”) typically involves placing aphysical object on a rotating platform inside a CT scanner between anx-ray source and x-ray detector and rotating the object around an axisof rotation to generate radiographs from the x-rays detected by thedetector. CT scanning thus produces radiographs with every pixel (x,y)containing the number I(x,y) of x-ray photons registered at the pixel(i.e. photons not absorbed by the scanned object).

Conventionally, the radiographs can be tomographically reconstructedinto a 3D representation of the object scanned (“CT reconstruction”).One example of CT reconstruction can be found in, for example, in thepublication Principles of Computerized Tomographic Imaging (A. C. Kakand Malcolm Slaney, Principles of Computerized Tomographic Imaging, IEEEPress, 1988), the entirety of which is incorporated by reference herein.Other types of CT reconstruction can also be performed.

CT reconstruction typically requires a total attenuation coefficientt(x,y) for every pixel of the radiograph, which in the case ofsingle-material object can proportional to the length of the path thex-ray travelled through the object. Conventional techniques fordetermining the total attenuation coefficient typically assume atheoretical relationship between detector readings and the attenuationcoefficients. This can produce undesirable artifacts in the 3Drepresentation of the object scanned, particularly for scanned objectsmade of different materials. Additionally, due to variability in thescanned object shape, making precise measurements of various pathlengths can be challenging. Finally, due to the number of differentpotential materials in the scanned object, developing a calibrationobject of simple shape for every single material can be challenging.

SUMMARY

Disclosed is a computer-implemented method of automatically determiningphoton-count to penetrated depth function for a CT reconstruction. Themethod includes performing one or more test CT reconstructions on one ormore radiographs, each test CT reconstruction using a test transferfunction, to provide one more test reconstructions and determining afinal transfer function from the one or more test reconstructions.

Disclosed is a system to automatically determine a photon-count topenetrated depth function for a CT reconstruction, the system including:a processor and a non-transitory computer-readable storage mediumcomprising instructions executable by the processor to perform stepsincluding: performing one or more test CT reconstructions on one or moreradiographs, each test CT reconstruction using a test transfer function,to provide one more test reconstructions; and determining a finaltransfer function from the one or more test reconstructions.

Disclosed is a non-transitory computer readable medium storingexecutable computer program instructions to automatically determine aphoton-count to penetrated depth function for a CT reconstruction, thecomputer program instructions including instructions for: performing oneor more test CT reconstructions on one or more radiographs, each test CTreconstruction using a test transfer function, to provide one more testreconstructions; and determining a final transfer function from the oneor more test reconstructions.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of a computed tomography (CT) scanningsystem in some embodiments.

FIG. 2 is a 2-dimensional (2D) radiographic image of a dental impressiontray containing a dental impression in some embodiments.

FIG. 3 is a cross-section of a 3-dimensional (3D) volumetric image insome embodiments.

FIG. 4 is a schematic diagram of portions of a CT scanning system insome embodiments.

FIGS. 5(a), 5(b), and 5(c) illustrate examples of radiographs in someembodiments for example.

FIG. 6 illustrates an example of a slice of a CT reconstructed volumegenerated in some embodiments.

FIG. 7 shows an example of block sampling in some embodiments.

FIG. 8 illustrates one example of inter-radiograph down-sampling togenerate down-sampled radiographs in some embodiments.

FIG. 9 illustrates an example of a histogram in some embodiments.

FIG. 10 illustrates an example of determining the location and height ofone or more peaks in some embodiments.

FIG. 11 illustrates an example of a histogram in some embodiments with ahighest peak and a second highest peak in some embodiments.

FIG. 12 is a graph showing an example various transfer functions in someembodiments.

FIG. 13 shows an example of a final CT reconstruction performed using areal transfer function in some embodiments.

FIG. 14 illustrates a flow diagram in some embodiments of acomputer-implemented method of automatically determining photon-count topenetrated depth function for a CT reconstruction.

FIG. 15 illustrates a processing system in some embodiments.

DETAILED DESCRIPTION

For purposes of this description, certain aspects, advantages, and novelfeatures of the embodiments of this disclosure are described herein. Thedisclosed methods, apparatus, and systems should not be construed asbeing limiting in any way. Instead, the present disclosure is directedtoward all novel and nonobvious features and aspects of the variousdisclosed embodiments, alone and in various combinations andsub-combinations with one another. The methods, apparatus, and systemsare not limited to any specific aspect or feature or combinationthereof, nor do the disclosed embodiments require that any one or morespecific advantages be present or problems be solved.

Although the operations of some of the disclosed embodiments aredescribed in a particular, sequential order for convenient presentation,it should be understood that this manner of description encompassesrearrangement, unless a particular ordering is required by specificlanguage set forth below. For example, operations described sequentiallymay in some cases be rearranged or performed concurrently. Moreover, forthe sake of simplicity, the attached figures may not show the variousways in which the disclosed methods can be used in conjunction withother methods. Additionally, the description sometimes uses terms like“provide” or “achieve” to describe the disclosed methods. The actualoperations that correspond to these terms may vary depending on theparticular implementation and are readily discernible by one of ordinaryskill in the art.

As used in this application and in the claims, the singular forms “a,”“an,” and “the” include the plural forms unless the context clearlydictates otherwise. Additionally, the term “includes” means “comprises.”Further, the terms “coupled” and “associated” generally meanelectrically, electromagnetically, and/or physically (e.g., mechanicallyor chemically) coupled or linked and does not exclude the presence ofintermediate elements between the coupled or associated items absentspecific contrary language.

In some examples, values, procedures, or apparatus may be referred to as“lowest,” “best,” “minimum,” or the like. It will be appreciated thatsuch descriptions are intended to indicate that a selection among manyalternatives can be made, and such selections need not be better,smaller, or otherwise preferable to other selections.

In the following description, certain terms may be used such as “up,”“down,” “upper,” “lower,” “horizontal,” “vertical,” “left,” “right,” andthe like. These terms are used, where applicable, to provide someclarity of description when dealing with relative relationships. But,these terms are not intended to imply absolute relationships, positions,and/or orientations. For example, with respect to an object, an “upper”surface can become a “lower” surface simply by turning the object over.Nevertheless, it is still the same object.

In one embodiment of the present disclosure, a computed tomography (CT)scanner uses x-rays to make a detailed image of an object. A pluralityof such images are then combined to form a 3D model of the object. Aschematic diagram of an example of a CT scanning system 140 is shown inFIG. 1 . The CT scanning system 140 includes a source of x-ray radiation142 that emits an x-ray beam 144. An object 146 being scanned is placedbetween the source 142 and an x-ray detector 148. In some embodiments,the object can be, for example, a triple-tray physical dental impressionor any other type of physical dental impression. In some embodiments,for example, any other type of physical dental impression can bescanned. In some embodiments, the object can be any object that can, forexample, fit in a CT scanning system and be penetrated by x-rays. Thex-ray detector 148, in turn, is connected to a processing system 150that is configured to receive the information from the detector 148 andto convert the information into a radiograph. Those skilled in the artwill recognize that the processing system 150 may comprise one or moreprocessors and/or computers that may be directly connected to thedetector, wirelessly connected, connected via a network, or otherwise indirect or indirect communication with the detector 148 and/or with theCT scanning system 140.

An example of a suitable scanning system 140 includes a Nikon Model XTH255 CT Scanner (Metrology) which is commercially available from NikonCorporation. The example scanning system includes a 225 kV microfocusx-ray source with a 3 μm focal spot size to provide high performanceimage acquisition and volume processing. The processing system 150 mayinclude a storage medium that is configured with instructions to managethe data collected by the scanning system. A particular scanning systemis described for illustrative purposes; any type/brand of CT scanningsystem can be utilized.

One example of CT scanning is described in U.S. Patent Application No.US20180132982A1 to Nikolskiy et al., which is hereby incorporated in itsentirety by reference. As noted above, during operation of the scanningsystem 140, the object 146 is located between the x-ray source 142 andthe x-ray detector 148. A series of images of the object 146 arecollected by the processing system 150 as the object 146 is rotated inplace between the source 142 and the detector 146. An example of asingle radiograph 160 is shown in FIG. 2 . The radiograph 160 and allradiographs described herein are understood to be digital. In oneembodiment, a series of 720 images are collected as the object 146 isrotated in place between the source 142 and the detector 148. In otherembodiments, more images or fewer images may be collected as will beunderstood by those skilled in the art.

Conventionally, the plurality of radiographs 160 of the object 146 aregenerated by and stored within a storage medium contained within theprocessing system 150 of the scanning system 140, where they may be usedby software contained within the processor to perform additionaloperations. For example, in an embodiment, the plurality of radiographs160 can undergo tomographic reconstruction in order to generate a 3Dvirtual image 170 (see FIG. 3 ) from the plurality of 2D radiographs 160generated by the scanning system 140. In the embodiment shown in FIG. 3, the 3D virtual image 170 is in the form of a volumetric image orvolumetric density file (shown in cross-section in FIG. 3 ) that isgenerated from the plurality of radiographs 160 by way of a CTreconstruction algorithm associated with the scanning system 140.

FIG. 4 is an illustration of portions of a CT scanning system asdiscussed previously. Certain features of the CT scanning system are notshown for clarity. Other conventional CT scanning systems known in theart can also be utilized. Conventionally, the physical object 146 to bescanned is placed inside the CT scanner on a rotational platform 202between an x-ray source 142 and x-ray detector 148. The physical object146 is exposed to x-rays generated by the x-ray source 142 that travelfrom the x-ray source 142 through the physical object 146 and to thex-ray detector 148. The x-ray detector 148 conventionally includes adetector pixel array (row of detector pixels and column of detectorpixels) which detects any incident x-rays to generate a radiograph, forexample. In some embodiments, the x-ray detector 148 can include anarray resolution of 1,000×1,000 pixels, for example. In someembodiments, the number of pixels can be at least 1 million pixels, forexample. Other numbers of pixels can also be present. Other arrayresolutions are also possible. Conventionally, as the physical object146 is rotated around an axis of rotation 204, the x-ray detector 148detects x-rays incident on each pixel such as detector pixel 210 (andany other detector pixels) at each rotational position to generatemultiple radiographs. The x-ray detector 148 can detect a photon countat each pixel for each radiograph generated at each rotational position.In some embodiments, the possible photon count can be any value. In someembodiments, the possible photon count range can be anywhere from 0 to65535 photons per pixel, for example. Other photon count ranges perpixel are also possible. In some embodiments, the physical object 146can be rotated 360 degrees once, and a direction of rotation 214 can beeither clockwise or counterclockwise. For example, detector pixel 222can experience the maximum photon count, I₀ in some embodiments sinceray 223 that does not pass through the object 146. In another example,detector pixel 224 can experience a lesser than maximum photon count, Iin some embodiments since ray 225 penetrates through the object 146. Thenumber of photons detected at detector pixel 224 can be based on alength path 228 the ray travels through the object 146.

Conventional/standard CT scanning systems allow setting the total numberof radiographs desired prior to scanning. Conventionally, the x-raydetector 148 detects and acquires a radiograph every rotational degreebased on the total number of radiographs desired. For example, therotational degree can conventionally be determined as follows by thestandard CT scanner: 360 degrees divided by the total number ofradiographs, for example. In some embodiments, the total number ofradiographs can be at least 500 radiographs, for example. The x-raydetector 148 conventionally detects and acquires the radiograph as wellas the photon count for every detector pixel such as detector pixel 210.An example of conventional photon counting and x-ray detectors can befound, for example, in Photon Counting and Energy Discriminating X-RayDetectors—Benefits and Applications (David WALTER, Uwe ZSCHERPEL, UweEWERT, BAM Bundesanstalt für Materialforschung und-prüfung, Berlin,Germany, 19^(th) World Conference on Non-Destructive Testing, 2016), theentirety of which is incorporated by reference herein. In someembodiments, the x-ray detector 148 can store the acquired radiographs.The axis of rotation 204 may not be visible, and is the axis aroundwhich the object rotates.

A single CT scan can therefore generate multiple radiographs in someembodiments in a single CT scan. CT scanning thus produces radiographswith every pixel (x,y) of a radiograph containing the number I(x,y) ofx-ray photons registered at the pixel (i.e. photons not absorbed by thescanned object).

FIGS. 5(a)-5(c) illustrate examples of a first radiograph 524, a secondradiograph 526, and a third radiograph 528, respectively, of themultiple radiographs. Three radiographs are shown for illustrationpurposes only; the plurality of radiographs can include any number ofradiographs, such as at least 500 radiographs, for example, in someembodiments. The first radiograph 524 can be the first radiograph pixelsdetected at a first rotational position, the second radiograph 526 canbe the second radiograph pixels detected at a second rotationalposition, and the third radiograph 528 can be the third radiographpixels detected at a third rotational position, for example. The nthradiograph can be the nth radiograph pixels detected at a nth rotationalposition as the physical object 146 is rotated around the axis ofrotation 204 from zero to a fixed number of degrees such as 360 degrees,in some embodiments, for example. The number of radiograph pixels shownis also for illustration purposes only, and can be greater or smaller invalue. In some embodiments, there can be 1,000 rows×1,000 columns ofpixels, for example.

CT reconstruction typically requires a total attenuation coefficientt(x,y) for every pixel of the radiograph, which in the case ofsingle-material object can be proportional to the length of the path thex-ray went through the object. However, CT scans can be of objects madeof multiple materials. Conventional techniques for determining the totalattenuation coefficient typically assume a theoretical relationshipbetween detector readings and the attenuation coefficients. This canproduce undesirable artifacts in the 3D representation of the objectscanned, particularly for scanned objects made of different materials.FIG. 6 illustrates an example of a slice 600 of a CT reconstructedvolume generated using conventional techniques. As can be seen, theslice 600 includes artifacts such as stokes 602 in empty regions and/oruneven density for different regions of the same object appearing in theslice such as object region 604 and object region 606. This can becaused by applying a theoretical transfer function, for example.

Some embodiments include a computer-implemented method of automaticallydetermining photon-count to penetrated depth function for a CTreconstruction. In some embodiments, the photon-count to penetrateddepth function can be referred to as a “transfer function”.

In some embodiments, automatically determining photon-count topenetrated depth function for a CT reconstruction can include performingone or more test CT reconstructions on one or more radiographs, eachtest CT reconstruction using a different test transfer function, toprovide one more test reconstructions. In some embodiments, thecomputer-implemented method receives the one or radiographs from a CTscan of an object. In some embodiments, the object can include one ormore materials, each of the materials having a different materialdensity. In some embodiments, the one or more radiographs can includeradiograph(s) of a physical dental impression. In some embodiments, thephysical dental impression can be any type of dental impression,including but not limited to a triple tray, full arch, double full arch,etc. In some embodiments, the physical impression can include one ormore materials such as a main impression material, a second impressionmaterial, and material of a plastic handle, for example. Other materialscan also be present in some embodiments. In some embodiments, theimpression itself can be made of multiple materials.

In some embodiments, the one or more radiographs can include one or moredown-sampled radiographs. In some embodiments, the computer-implementedmethod generates the one or more down-sampled radiographs. In someembodiments, the computer-implemented method can receive the one or moredown-sampled radiographs. In some embodiments, the one or moredown-sampled radiographs are generated prior to generating one or moretest CT reconstructions. In some embodiments, the one or moredown-sampled radiographs can be generated prior to performing the finalCT reconstruction. The one or more down-sampled radiographs can reducethe amount of input data to allow more reconstructions during some timeperiod compared to not down-sampled, full resolution mode.

In some embodiments, the one or more down-sampled radiographs can begenerated by block sampling. In some embodiments, block sampling caninclude replacing a block of pixels (also known as “multi-pixel block”)within each of the one or more radiographs with a single blockrepresentative pixel. The block of pixels can include two or morepixels, and down-sampling can provide a reduction of resolution of theradiograph. The block of pixels can include a square block of pixelswithin a radiograph in some embodiments, for example. In someembodiments, the block sampled radiograph can include a blockrepresentative pixel for each block of the original radiograph. In someembodiments, the block representative pixel can be a mean value ofpixels in the block of pixels. In some embodiments, the blockrepresentative pixel can be an average of the value in the block ofpixels. In some embodiments, the block representative pixel can be anyvalue that combines or uses the values in the block of pixels. In someembodiments, down-sampling reduces a resolution of the one or moreradiographs.

FIG. 7 illustrates an example of block sampling, where a radiograph 702is block sampled to provide down-sampled radiograph 704. As illustratedin the example, a multi-pixel block 712 can include two or more pixels.Multi-pixel block 712 includes, for example, 4×4 pixels, including pixel703. Block sampling can down sample the multi-pixel block 712 into asingle block representative pixel 714, for example. In some embodiments,the representative pixel 714 can include a mean value of pixels in themulti-pixel block 712. In some embodiments, the representative pixel 712can be an average of the value in the multi-pixel block 712. In someembodiments, the representative pixel 714 can be any value that combinesor uses the values in the multi-pixel block 712. Additional multi-pixelblocks can be reduced to their respective single block representativepixels. In some embodiments, the entire radiograph 702 can be dividedinto several multi-pixel blocks, and each multi-pixel block sampled toprovide its respective single block representative pixel in thedown-sampled radiograph 704, for example. In the example, radiograph 702is reduced by 16 times to provide block sampled radiograph 704. Forexample, radiograph 702 has a resolution of 96 pixels, and block sampledradiograph 704 has a resolution of 6 pixels. The number and arrangementof pixels in the example is for illustrative purposes only, and canvary.

In some embodiments, the one or more down-sampled radiographs can begenerated by inter-radiograph down-sampling. In some embodiments,inter-radiograph down-sampling can include generating one or moredown-sampled radiographs by selecting fewer than the total number ofradiographs produced by a CT scan. In some embodiments, inter-radiographdown-sampling can include generating the one or more down-sampledradiographs by replacing one or more consecutive CT scanner radiographswith a single representative radiograph. In some embodiments, the singlerepresentative radiograph can include one or more positionalrepresentative pixels of each corresponding pixel position across one ormore radiographs. In some embodiments, the positional representativepixel can be a mean value of pixels at a pixel position across one ormore radiographs. In some embodiments, the positional representativepixel can be an average of pixels at a pixel position across one or moreradiographs. In some embodiments, the positional representative pixelcan be any value that combines or uses the values of pixels at a pixelposition across one or more radiographs. In some embodiments,inter-radiograph down-sampling reduces a resolution of the one or moreradiographs.

FIG. 8 illustrates one example of inter-radiograph down-sampling togenerate down-sampled radiographs by replacing one or more consecutiveCT scanner radiographs with a single representative radiograph. Thefigure illustrates four consecutive radiographs from a CT scan: firstradiograph 802, second radiograph 804, third radiograph 806, and fourthradiograph 808. Four radiographs are shown for illustrative purposesonly. More or fewer radiographs can be used. The computer-implementedmethod can down-sample the consecutive radiographs by generating apositional representative pixel for each pixel position across theconsecutive radiographs. For example, the first radiograph 802 caninclude a first radiograph pixel 812 at an x,y position in the firstradiograph 802. Second radiograph 804 can include a second radiographpixel 814 at the same x,y position as the first radiograph pixel 812,but located in the second radiograph 804. Similarly, third radiograph806 can include a third radiograph pixel 816 at the same x,y position asthe first radiograph pixel 812 and the second radiograph pixel 814, butlocated in the third radiograph 806. Finally, fourth radiograph 808 caninclude a fourth radiograph pixel 818 at the same x,y position as thefirst radiograph pixel 812, the second radiograph pixel 814, and thethird radiograph pixel 816, but located in the fourth radiograph 808. Insome embodiments, the first radiograph 802, the second radiograph 804,the third radiograph 806, and the fourth radiograph 808 can be replacedwith a single representative radiograph 820. The single representativeradiograph 820 can include one or more down-sampled pixels such aspositional representative pixel 822. Positional representative pixel 822can be an average of pixel values at its same x,y position but inconsecutive radiographs, for example. For example, the positionalrepresentative pixel 822 value can be an average of the first radiographpixel 812 value, the second radiograph pixel 814 value, the thirdradiograph pixel 816 value, and the fourth radiograph pixel 818 valuesince these pixels are all in the same x,y position in their respectiveradiographs.

In some embodiments, one or more pixels in the representative imagegenerated by inter-radiograph down-sampling are down-sampled pixels. Forexample, while only one positional representative pixel 822 is shown forillustrative purposes, the representative image 820 can include manymore (including all) down-sampled pixels. In some embodiments,inter-radiograph down-sampling reduces the number of total radiographpixels by 64 times where 4 consecutive radiographs are inter-radiographdown-sampled.

In some embodiments, the one or more down-sampled radiographs can begenerated by reducing a reconstruction image resolution. In someembodiments, reducing the reconstruction image can include reducing thereconstruction image to correspond to the one or more down-sampledprojection images. In some embodiments, the reconstruction resolution ofthe volumetric reconstructed image is reduced by the same factor alongeach dimension as the one or more down-sampled projection images. Insome embodiments, the reconstruction resolution is reduced by the samefactor along x,y,z axes to match the resolution of the one or moredown-sampled projection images. In some embodiments, the number ofoperations performed by the Filtered Back Projection (FBP)reconstruction algorithm is proportional to the number of voxels in thevolume times the number of input projections.

In some embodiments, radiographs from the CT scan be down-sampled usinga single down-sampling technique, or any combination of down-samplingtechniques such as block sampling, inter-radiograph down-sampling,and/or reconstruction resolution sampling.

As an example, combining inter-radiograph sampling of 4 radiographs andreconstruction resolution sampling by 4 in each dimension (x,y,z), thereconstruction time can be theoretically speed up by 4*4*4*4=256 times,for example. In some embodiments, the sped up reconstruction time allowsmore reconstructions and estimations of more transfer functions.

In some embodiments, automatically determining photon-count topenetrated depth function for a CT reconstruction can include performingone or more test CT reconstructions on one or more radiographs, eachtest CT reconstruction using a different test transfer function, toprovide one more test reconstructions.

In some embodiments, the computer-implemented method can select atransfer function from a multi-parameter function family t(a, b, c, d, .. . ). In some embodiments, the real transfer function t can include apolynomial of theoretical transfer function:

$u = {1 - {\frac{\ln I}{\ln I_{0}}:}}$

In some embodiments, each test transfer function can include one or morecoefficients t(a, b, c, d, . . . )=au+bu²+cu³+du⁴+ . . . , wherea+b+c+d+ . . . =1. In some embodiments, the best parameters for thetransfer function can be determined using any non-linear optimizationtechnique known in the art. One example of a non-linear optimizationtechnique known in the art can include, for example, theLevenberg-Marquardt Method described in NUMERICAL RECIPES IN C: THE ARTOF SCIENTIFIC COMPUTING, by William H. Press, Brian P. Flannery, Saul A.Teukolsky, and William Vetterling, Cambridge University Press; 2^(nd)Edition, (C) 1988-1992, which is hereby incorporated by reference in itsentirety. In some embodiments, the one or more test CT reconstructionscan be performed using parameters for the transfer function by tryingall values of parameters in certain domain and with certain step, e.g.

-   -   a∈[0, 0.05, 0.1, . . . 1],    -   b∈[−6, −5.75, −5.5, . . . 6],    -   c∈[−12, −11, −10, . . . 12],    -   d=1−a−b−c

In some embodiments, upon defining the one or more numeric parameterssuch as a, b, c, d, . . . , the computer-implemented method reconstructsa volumetric image based on the transfer function t(a, b, c, d, . . . )to generate one or more test CT reconstructions. In some embodiments,the computer-implemented method can perform the test CT reconstructions.In some embodiments, the test CT reconstructions can be generated byanother external process. In some embodiments, a test CT reconstructionis performed for each test transfer function using one or moreradiographs produced by CT scanning. In some embodiments, a test CTreconstruction is performed for each test transfer function on one ormore down-sampled radiographs. In some embodiments, multiple test CTreconstructions are performed.

In some embodiments, the computer-implemented method can perform one ormore test CT reconstructions using any CT reconstruction technique knownin the art. In some embodiments, the computer-implemented method canperform test CT reconstructions. In some embodiments, thecomputer-implemented method can perform conventional CT reconstruction,which can include conventional filtering and conventionalback-projection. One type of conventional CT reconstruction algorithmcan be the filtered back projection algorithm as described in thePrinciples of Computerized Tomographic Imaging publication. ConventionalCT reconstruction is also described in Held, Devin, Analysis of 3DCone-Beam CT Image Reconstruction Performance on a FPGA (2016).Electronic Thesis and Dissertation Repository, 4349, the entirety ofwhich is hereby incorporated by reference. The conventional CTreconstruction algorithm can be referred to as the FeldkampReconstruction Algorithm, and is described in U.S. Pat. No. 5,375,156Ato Kuo-Petravic et al., issued Dec. 20, 1994, the entirety of which ishereby incorporated by reference. Other types of CT reconstructionalgorithms known in the art can also be used.

In some embodiments, the computer-implemented method can performconventional filtering of the one or more radiographs received. In someembodiments, the one or more radiographs can be down-sampledradiographs. Filtering conventionally involves applying a filteringfunction such as a ramp function or other type of filtering functionknown in the art to each row of the radiograph. Filtering is known inthe art. For example, one or more filtering functions are described inFILTERING IN SPECT IMAGE RECONSTRUCTION, by Maria E. Lyra and AgapiPloussi, Article in International Journal of Biomedical Imaging, Volume2011, Article ID 693795, June 2011, which is hereby incorporated byreference in its entirety. In some embodiments filtering can includeapplying a filter function to the one or more radiograph rows to provideone or more filtered rows. Any type of CT reconstruction filteringfunction known in the art can be applied. In some embodiments, applyinga filtering function can include convolving each row of the radiographwith the filter function to provide a filtered radiograph. In someembodiments, for example, a ramp filtering function can be applied. Anyother filter known in the art can be applied in some embodiments, forexample. In some embodiments, filtering is done per each row of theradiograph. In some embodiments, filtering is performed on the entireradiograph at once.

In some embodiments, the computer-implemented method can back-projectone or more filtered radiographs using conventional back projectiontechniques known in the art. In some embodiments, the filteredradiographs can be filtered down-sampled radiographs. Back projection isconventionally known, and can include, in some embodiments, smearingback the one or more filtered radiographs on to the reconstructionvolume. For example, in some embodiments, the smearing back is along thesame rays joining in x-ray source position to hit detector pixels.

As an example, conventional back-projection can include the followingsteps. For each voxel of the volume being reconstructed, thecomputer-implemented method can determine a line that passes via thecenter of the voxel and the x-ray source point, considering that thex-ray source point changes location relative to the object with therotation of the rotation table. The computer-implemented method can finda detector point where the line hits the detector. Thecomputer-implemented method can take the value of the filtered imagefrom this detector location and add it to the current voxel with anappropriate weight. The computer-implemented method can repeat the stepsfor all voxels and all projections.

For example, back-projecting for a cone-beam x-ray source isconventionally known as follows, which is back projecting a value thatis bilinearly interpolated from a grid of Q_(β)(p,ξ):

g(t,s,z)=∫₀ ^(2π)(D ² _(S0)/(D _(S0) −s)²)Q _(β)(D _(SO) t/(D _(S0)−s)),(D _(SOZ)/(D _(SO) −s)))dβ

p=p′D _(S0) /D _(S0) +D _(DE)

ξ=ξ′D _(S0) /D _(S0) +D _(DE)

where (t,s,z) is the original coordinate system, D_(S0) is the source torotation axis distance, D_(DE) is the rotation axis-to-detectordistance, so the sum D_(S0)+D_(DE) is the distance from the source tothe detector, and β is the angular differential change.

Other techniques for performing filtering and back projection known inthe art can also be used by the computer-implemented method. In thismanner, several test CT reconstructions can be generated.

In some embodiments, the computer-implemented method can determine areal transfer function from the one or more test CT reconstructions. Insome embodiments, determining the real transfer function can includedetermining a quality of the one or more test reconstructions. In someembodiments, determining the real transfer function can includedetermining a highest quality test reconstruction from the one or moretest reconstructions. In some embodiments, determining the quality of aparticular test reconstruction of the one or more test reconstructionscan include determining a density histogram of voxel values in theparticular test reconstruction.

In some embodiments, the density histogram can include determining afrequency distribution of all voxel values within the volumetric densityfile.

In some embodiments, the histogram can provide a frequency distributionof air and material densities in a reconstruction volume. For example,in some embodiments, the reconstruction volume can be a test CTreconstruction volume. In some embodiments, the reconstruction volumecan be received by the computer-implemented system. In some embodiments,the reconstruction volume can be a volumetric density file that containsvoxels having density information of one or more materials andsurrounding air from a CT scan. The number of voxels at a particulardensity value can represent the amount of the material/air having thatparticular density.

As illustrated in the histogram 911 of FIG. 9 , in some embodiments, thecomputer-implemented method can generate a density frequencydistribution of the volumetric density file. In some embodiments, thevolumetric density file can be that of a test CT reconstruction. In someembodiments, the volumetric density file can be of a final CTreconstruction. The histogram 911 is shown for illustrative purposes andincludes an x-axis 913 of density values and the y-axis 914 of thenumber of voxels (voxel counts), for example. All histogramsillustrating the density frequency distribution herein include an x-axisof density values and a y-axis of the number of voxels (voxel counts).In some embodiments, the computer-implemented method can generate anormalized scan density range 901 for the volumetric density file. Forexample, in some embodiments, the computer-implemented method cangenerate the normalized scan density range 901 to be between 0.0 and1.0. The computer-implemented method can subdivide the normalized scandensity range into one or more scan density subranges 903 (scan densitysubrange 903 is shown among multiple scan density subranges in amagnified view). For example, the computer-implemented method cansubdivide the normalized scan density range 901 of 0.0 and 1.0 intomultiple scan density subranges 903. In some embodiments, each subrangecan be numbered starting from 1 to the total number of subranges in thescan density range 901. In some embodiments, the number of scan densitysubranges 903 can be 500, for example. In some embodiments, more orfewer scan density subranges 903 are possible. For each voxel, thecomputer-implemented method normalizes the density value of the voxel tofall within the normalized scan density range 901. Thecomputer-implemented method compares the normalized density of the voxelwith the one or more scan density subranges 903 and increments the voxelcount for the scan density subrange 903 within which the normalizedvoxel density value falls. The computer-implemented method loads thenext voxel from the volumetric density file and repeats the process forevery voxel in the volumetric density file to determine the total voxelcount for each of the scan density subranges 903. In some embodiments,the computer-implemented method takes a logarithm of the voxel countsfor each scan density subrange 903. The subrange can also be referred toas a “bin”, with the subrange number corresponding to a bin number. Thecomputer-implemented method in this manner can generate the densityfrequency distribution which is depicted as histogram 911 forillustrative purposes for one or more of the test CT reconstructions.

In some embodiments, determining the quality of the particular testreconstruction of the one or more test reconstructions can includedetermining a precise location and a height of one or more peaks in thedensity histogram of the particular test reconstruction. In someembodiments, the one or more peaks can include a highest peak. In someembodiments, the highest peak corresponds to air density. In someembodiments, the one or more peaks can include a second highest peak. Insome embodiments, the second highest peak corresponds to a main materialdensity.

FIG. 9 illustrates a first highest peak 922 and a second highest peak924. In some embodiments, the first highest peak 922 can correspond toair density and the second highest peak 924 can correspond to a mainmaterial density.

In some embodiments, determining the precise location and height of theone or more peaks can include determining a precise density value and aprecise peak height at the density value for the peak. In someembodiments, the precise location can be a density value that is afloating point density value. In some embodiments, the precise locationdensity value can be determined from a bin number of the peak. The binnumber of the peak can be an integer value. In some embodiments theinteger valued location of a peak is its bin (subrange) number.

In some embodiments, the computer-implemented method can determine apeak bin number for a peak. The computer-implemented method candetermine a local maximum peak bin and a pair of lower density bins tothe immediate left of the peak bin in the histogram (i.e. having densityvalues less than the peak bin) and a pair of higher density bins to theimmediate right of the peak bin in the histogram (i.e. having densityvalues greater than the peak bin). The computer-implemented method candetermine a best parabola approximating the five points of the peak binvalues. The five points can include the local maximum peak bin, the pairof lower density bins to the left of the peak bin and the pair of higherdensity bins to the right of the peak bin. In some embodiments, thecomputer-implemented method can determine a location of the parabolamaximum and its value as the height of the peak and it's position as thelocation of the peak. In some embodiments, determining the location andheight of the one or more peaks can include determining the location andheight of the highest peak and the second highest peak.

FIG. 10 illustrates an example of determining the location and height ofone or more peaks in some embodiments. The figure shows a portion of ahistogram (frequency distribution) 1000 with five bins with a peak bin1002. Peak bin 1002 can be either the highest peak or the second highestpeak. The same process can be applied to both the highest peak and thesecond highest peak to determine their exact position and height. As canbe seen in the figure, the computer-implemented method determines a pairof lower density bins 1004 adjacent to left of the peak bin 1002 in thehistogram. The pair of lower density bins 1004 have a density valuesless than the peak bin 1002. The computer-implemented also determines apair of higher density bins 1006 to right of the peak bin 1002 in thehistogram. The pair of higher density bins 1006 have density valueshigher than the peak bin 1002. The computer-implemented method candetermine a best fit parabola 1010 through the pair of lower densitybins 1004, the peak bin 1002, and the pair of higher density bins 1006.The computer-implemented method can determine the precise location andheight of the peak 1012 from the highest point of the best fit parabola1010.

As illustrated in FIG. 11 , the computer-implemented method candetermine the exact location and height of the highest peak 1102 and thesecond highest peak 1104.

In some embodiments, determining the quality of the one or more testreconstructions can include determining, for a particular testreconstruction, the quality of the reconstruction, q, as follows:

q=h _(m)(d _(m) −d _(a))/(d _(max) −d _(min))

In some embodiments, the histogram can include a minimum density d_(min)to maximum density d_(max) and given air peak location d_(a) and mainmaterial location d_(m) and height h_(m). In some embodiments, thehighest quality test reconstruction is the one with the greatest qvalue. In some embodiments, the quality is determined for at least oneof the one or more test reconstructions. In some embodiments, thequality is accordingly determined for each test transfer function, eachtest transfer function having parameter values a, b, c, d, . . . . Insome embodiments, the computer-implemented method determines the qualityas a non-linear function of the parameters q(a, b, c, d, . . . ). Insome embodiments, the quality is determined for all of the one or moretest reconstructions. In some embodiments, the computer-implementedmethod determines the best quality (highest q) from the testreconstructions to determine the best test reconstruction. In someembodiments, the computer-implemented method selects the transferfunction corresponding to the best test reconstruction as the realtransfer function on which to perform final CT reconstruction.

FIG. 12 shows one example of transfer functions such as a theoreticaltransfer function 1202, where t=u, a manually set transfer function1204, where t=0.2u+0.8u², and a real transfer function 1206, wheret=0.25u+5.75u²−11u³+6u⁴. These example transfer functions are shown forillustrative purposes only, and the disclosure is not limited to or bythese example transfer functions. Other transfer functions are possible.

FIG. 13 shows an example of a final CT reconstruction with reduced oreliminated stokes and with consistent density for the same material inthe reconstructed volume. The final CT reconstruction is forillustrative purposes only, and the disclosure is not limited to or bythe example illustrated in FIG. 13 .

In some embodiments, once the computer-implemented method determines thereal transfer function, the computer-implemented method can perform afinal CT reconstruction using the real transfer function and theradiographs from CT scanning (not down-sampled radiographs). In someembodiments, the computer-implemented method provide the real transferfunction to another process that can perform the final CTreconstruction.

In some embodiments, the entire process can be automated—without userinput. For example, the computer-implemented method can receive one ormore radiographs, automatically perform optional down-sampling,automatically generate one or more test reconstructions, automaticallydetermine the best test reconstruction, automatically determine the realtransfer function, and optionally automatically perform final CTreconstruction using the real transfer function.

FIG. 14 illustrates a flow diagram in some embodiments of acomputer-implemented method of automatically determining photon-count topenetrated depth function for a CT reconstruction. Thecomputer-implemented method can include performing one or more test CTreconstructions on one or more radiographs, each test CT reconstructionusing a test transfer function, to provide one more test reconstructionsat 1402 and determining a final transfer function from the one or moretest reconstructions at 1404. In some embodiments, the one or moreradiographs comprise one or more down-sampled radiographs. In someembodiments, the one or more down-sampled radiographs are generatedprior to generating one or more test CT reconstructions. In someembodiments, the one or more down-sampled radiographs are generated byreplacing a block of pixels in each of one or more CT scannerradiographs with a single representative pixel. In some embodiments, oneor more down-sampled radiographs are generated by replacing one or moreconsecutive CT scanner radiographs with a single representativeradiograph. In some embodiments, determining the final transfer functioncomprises determining a quality of the one or more test reconstructions.In some embodiments, determining the quality of a particular testreconstruction of the one or more test reconstructions comprisesdetermining a highest peak location and height and a second highest peaklocation and height in a density histogram of the particular testreconstruction.

FIG. 15 illustrates a processing system 14000 in some embodiments. Thesystem 14000 can include a processor 14030, computer-readable storagemedium 14034 having instructions executable by the processor to performone or more steps described in the present disclosure.

One or more advantages of one or more features can include, for example,reduction or elimination of undesirable artifacts in the 3Drepresentation of the object scanned, particularly for scanned objectsmade of different materials. One or more advantages of one or morefeatures can include allowing reconstruction without requiring precisemeasurements of various path lengths. One or more advantages of one ormore features can include, for example, reconstruction of an object madeof different. One or more advantages of one or more features caninclude, for example, reconstruction without developing a calibrationobject. One or more advantages of one or more features can include, forexample, automatic determination of a real transfer function. One ormore advantages of one or more features can include, for example, fastgeneration of test reconstructions using down-sampled radiographs. Oneor more advantages of one or more features can include, for example,improved reconstruction accuracy. One or more advantages of one or morefeatures can include, for example, reduction or elimination of artifactssuch as stokes and/or other artifacts One or more advantages of one ormore features can include, for example, reduction or elimination ofdifferent density values for the same material in the reconstruction.

One or more of the features disclosed herein can be performed and/orattained automatically, without manual or user intervention. One or moreof the features disclosed herein can be performed by acomputer-implemented method. The features—including but not limited toany methods and systems—disclosed may be implemented in computingsystems. For example, the computing environment 14042 used to performthese functions can be any of a variety of computing devices (e.g.,desktop computer, laptop computer, server computer, tablet computer,gaming system, mobile device, programmable automation controller, videocard, etc.) that can be incorporated into a computing system comprisingone or more computing devices. In some embodiments, the computing systemmay be a cloud-based computing system.

For example, a computing environment 14042 may include one or moreprocessing units 14030 and memory 14032. The processing units executecomputer-executable instructions. A processing unit 14030 can be acentral processing unit (CPU), a processor in an application-specificintegrated circuit (ASIC), or any other type of processor. In someembodiments, the one or more processing units 14030 can execute multiplecomputer-executable instructions in parallel, for example. In amulti-processing system, multiple processing units executecomputer-executable instructions to increase processing power. Forexample, a representative computing environment may include a centralprocessing unit as well as a graphics processing unit or co-processingunit. The tangible memory 14032 may be volatile memory (e.g., registers,cache, RAM), non-volatile memory (e.g., ROM, EEPROM, flash memory,etc.), or some combination of the two, accessible by the processingunit(s). The memory stores software implementing one or more innovationsdescribed herein, in the form of computer-executable instructionssuitable for execution by the processing unit(s).

A computing system may have additional features. For example, in someembodiments, the computing environment includes storage 14034, one ormore input devices 14036, one or more output devices 14038, and one ormore communication connections 14037. An interconnection mechanism suchas a bus, controller, or network, interconnects the components of thecomputing environment. Typically, operating system software provides anoperating environment for other software executing in the computingenvironment, and coordinates activities of the components of thecomputing environment.

The tangible storage 14034 may be removable or non-removable, andincludes magnetic or optical media such as magnetic disks, magnetictapes or cassettes, CD-ROMs, DVDs, or any other medium that can be usedto store information in a non-transitory way and can be accessed withinthe computing environment. The storage 14034 stores instructions for thesoftware implementing one or more innovations described herein.

The input device(s) may be, for example: a touch input device, such as akeyboard, mouse, pen, or trackball; a voice input device; a scanningdevice; any of various sensors; another device that provides input tothe computing environment; or combinations thereof. For video encoding,the input device(s) may be a camera, video card, TV tuner card, orsimilar device that accepts video input in analog or digital form, or aCD-ROM or CD-RW that reads video samples into the computing environment.The output device(s) may be a display, printer, speaker, CD-writer, oranother device that provides output from the computing environment.

The communication connection(s) enable communication over acommunication medium to another computing entity. The communicationmedium conveys information, such as computer-executable instructions,audio or video input or output, or other data in a modulated datasignal. A modulated data signal is a signal that has one or more of itscharacteristics set or changed in such a manner as to encode informationin the signal. By way of example, and not limitation, communicationmedia can use an electrical, optical, RF, or other carrier.

Any of the disclosed methods can be implemented as computer-executableinstructions stored on one or more computer-readable storage media 14034(e.g., one or more optical media discs, volatile memory components (suchas DRAM or SRAM), or nonvolatile memory components (such as flash memoryor hard drives)) and executed on a computer (e.g., any commerciallyavailable computer, including smart phones, other mobile devices thatinclude computing hardware, or programmable automation controllers)(e.g., the computer-executable instructions cause one or more processorsof a computer system to perform the method). The term computer-readablestorage media does not include communication connections, such assignals and carrier waves. Any of the computer-executable instructionsfor implementing the disclosed techniques as well as any data createdand used during implementation of the disclosed embodiments can bestored on one or more computer-readable storage media 14034. Thecomputer-executable instructions can be part of, for example, adedicated software application or a software application that isaccessed or downloaded via a web browser or other software application(such as a remote computing application). Such software can be executed,for example, on a single local computer (e.g., any suitable commerciallyavailable computer) or in a network environment (e.g., via the Internet,a wide-area network, a local-area network, a client-server network (suchas a cloud computing network), or other such network) using one or morenetwork computers.

For clarity, only certain selected aspects of the software-basedimplementations are described. Other details that are well known in theart are omitted. For example, it should be understood that the disclosedtechnology is not limited to any specific computer language or program.For instance, the disclosed technology can be implemented by softwarewritten in C++, Java, Perl, Python, JavaScript, Adobe Flash, or anyother suitable programming language. Likewise, the disclosed technologyis not limited to any particular computer or type of hardware. Certaindetails of suitable computers and hardware are well known and need notbe set forth in detail in this disclosure.

It should also be well understood that any functionality describedherein can be performed, at least in part, by one or more hardware logiccomponents, instead of software. For example, and without limitation,illustrative types of hardware logic components that can be used includeField-programmable Gate Arrays (FPGAs), Program-specific IntegratedCircuits (ASICs), Program-specific Standard Products (ASSPs),System-on-a-chip systems (SOCs), Complex Programmable Logic Devices(CPLDs), etc.

Furthermore, any of the software-based embodiments (comprising, forexample, computer-executable instructions for causing a computer toperform any of the disclosed methods) can be uploaded, downloaded, orremotely accessed through a suitable communication means. Such suitablecommunication means include, for example, the Internet, the World WideWeb, an intranet, software applications, cable (including fiber opticcable), magnetic communications, electromagnetic communications(including RF, microwave, and infrared communications), electroniccommunications, or other such communication means.

In view of the many possible embodiments to which the principles of thedisclosure may be applied, it should be recognized that the illustratedembodiments are only examples and should not be taken as limiting thescope of the disclosure.

What is claimed is:
 1. A computer-implemented method of automatically determining photon-count to penetrated depth function for a CT reconstruction, comprising: performing one or more test CT reconstructions on one or more radiographs, each test CT reconstruction using a test transfer function, to provide one more test reconstructions; and determining a final transfer function from the one or more test reconstructions.
 2. The method of claim 1, wherein the one or more radiographs comprise one or more down-sampled radiographs.
 3. The method of claim 2, wherein the one or more down-sampled radiographs are generated prior to generating one or more test CT reconstructions.
 4. The method of claim 2, wherein the one or more down-sampled radiographs are generated by replacing a block of pixels in each of one or more CT scanner radiographs with a single representative pixel.
 5. The method of claim 2, wherein the one or more down-sampled radiographs are generated by replacing one or more consecutive CT scanner radiographs with a single representative radiograph.
 6. The method of claim 1, wherein determining the final transfer function comprises determining a quality of the one or more test reconstructions.
 7. The method of claim 6, wherein determining the quality of a particular test reconstruction of the one or more test reconstructions comprises determining a highest peak location and height and a second highest peak location and height in a density histogram of the particular test reconstruction.
 8. A system to automatically determine a photon-count to penetrated depth function for a CT reconstruction, the system comprising: a processor; and a non-transitory computer-readable storage medium comprising instructions executable by the processor to perform steps comprising: performing one or more test CT reconstructions on one or more radiographs, each test CT reconstruction using a test transfer function, to provide one more test reconstructions; determining a final transfer function from the one or more test reconstructions.
 9. The system of claim 8, wherein the one or more radiographs comprise one or more down-sampled radiographs.
 10. The system of claim 9, wherein the one or more down-sampled radiographs are generated prior to generating one or more test CT reconstructions.
 11. The system of claim 9, wherein the one or more down-sampled radiographs are generated by replacing a block of pixels in each of one or more CT scanner radiographs with a single representative pixel.
 12. The system of claim 10, wherein the one or more down-sampled radiographs are generated by replacing one or more consecutive CT scanner radiographs with a single representative radiograph.
 13. The system of claim 8, wherein determining the final transfer function comprises determining a quality of the one or more test reconstructions.
 14. The system of claim 13, wherein determining the quality of a particular test reconstruction of the one or more test reconstructions comprises determining a highest peak location and height and a second highest peak location and height in a density histogram of the particular test reconstruction.
 15. A non-transitory computer readable medium storing executable computer program instructions to automatically determine a photon-count to penetrated depth function for a CT reconstruction, the computer program instructions comprising instructions for: performing one or more test CT reconstructions on one or more radiographs, each test CT reconstruction using a test transfer function, to provide one more test reconstructions; determining a final transfer function from the one or more test reconstructions.
 16. The medium of claim 15, wherein the one or more radiographs comprise one or more down-sampled radiographs.
 17. The medium of claim 16, wherein the one or more down-sampled radiographs are generated prior to generating one or more test CT reconstructions.
 18. The medium of claim 16, wherein the one or more down-sampled radiographs are generated by replacing one or more consecutive CT scanner radiographs with a single representative radiograph.
 19. The medium of claim 15, wherein determining the final transfer function comprises determining a quality of the one or more test reconstructions.
 20. The medium of claim 19, wherein determining the quality of a particular test reconstruction of the one or more test reconstructions comprises determining a highest peak location and height and a second highest peak location and height in a density histogram of the particular test reconstruction. 